Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink]
17 Jun 2013, 23:40

1

This post received KUDOS

Expert's post

Smita04 wrote:

If xy < 4, is x < 2 ?

(1) y > 1 (2) y > x

From F.S 1, when y = 4, x = 0.5, xy<4 and x<2.Hence a YES for the question stem. However, for y = 3/2 and x = 2, xy<4 and x=2, hence a NO for the question stem.Insufficient.

From F. S 2, we know that y>x.

Had y been equal to x, we would have x*x<4 --> |x|<2 --> -2<x<2

However, as y>x, to maintain the above given inequality, the value of x will have to reduce even further. Thus, x <2. Sufficient.

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink]
27 Jul 2013, 20:52

nguyenduong wrote:

- A is insufficient. - Option B. what if x or y is negative integer. I don't see you mentioned it in your answer.

nguyenduong,

Interpretation should be based on given (true) statements. Given here xy<4 and for pt. (2) y>x.

Take any signs, y has to be greater than x or greater part of the multiplication with x resulting in a product smaller than 4. Consider if xy was 4 (xy=4) and y=x then both x & y would have been + /- 2. Now when the product reduces (product < 4), x has to be always less than the equal contribution i.e. 2.

Hope I could explain. _________________

------- IaintGivinUp! GMAT assassins aren't born, they are made.

Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink]
28 Jul 2013, 03:48

Expert's post

nguyenduong wrote:

- A is insufficient. - Option B. what if x or y is negative integer. I don't see you mentioned it in your answer.

The question asks whether x<2. Now, for (2) if x is negative, then x<0<2 and if y is negative, then x<y<0<2. In either case we have an YES answer to the question. _________________

Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink]
06 Aug 2014, 06:50

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink]
15 Jul 2015, 10:53

getbetter wrote:

Hi Folks, does the method below looks ok?

1) xy <4 -4y<-4 y(x-4) <0 y<0 and x < 4 not suff

2) xy<4 xy^2 <4y 4x < 4y x(y^2 -4) <0

x <0 suff.

1) Where are you getting the above text in red from? How do you get y (x-4) < 0 ? Even if I assume that what you have written in correct, where are you getting y<0 from?

2) Text in blue is only possible if y>0. You need to reverse the inequality if y <0. Statement 2 just mentions that y>x and it does not tell us that x>0 to make y>0 at the same time. Also, how are you getting x(y^2-4)<0 from 4x<4y?

Based on your solution, you were lucky to get to the correct answer and it does not look correct. Maybe, if you could write out all the steps clearly, we can take a look again. _________________

If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink]
15 Jul 2015, 15:09

1

This post received KUDOS

getbetter wrote:

Sure let me explain step by step:

1) xy <4 ———(1)

y > 1 -> 1<y -> -y<-1 multiply both sides by 4 : -4y<-4 ————(2)

(1)+(2) xy - 4y < 0 y(x-4) <0 y<0 and x < 4 not suff.

2) xy<4

multiply both sides by ‘y’: xy^2 < 4y ————(1) y > x Multiply both sides by 4: 4x < 4y —————(2)

(1)-(2):

x(y^2 -4) <0

x <0 suff.

Ok, this looks better now.

Text in green: correct! Text in red: incorrect

1) xy <4 ———(1)

y > 1 -> 1<y -> -y<-1 multiply both sides by 4 : -4y<-4 ————(2)

(1)+(2) xy - 4y < 0 y(x-4) <0 ------ (3) y<0 and x < 4 not suff.

From 3, you know that y (x-4)<0 ---> this means 2 cases:

either y<0 and x>4 (not possible as given y>1) or y>0 and x<4 . Even if we have x<4, x can be 3 or 1.5 , thus x <2 may or may not be true. Thus this statement is not sufficient.

2) xy<4

multiply both sides by ‘y’: xy^2 < 4y ————(1) y > x Multiply both sides by 4: 4x < 4y —————(2)

(1)-(2):

x(y^2 -4) <0

x <0 suff.

How do you know whether y < or > 0 when you multiply xy<4 by y? if y is >0 then yes what you did is correct, but if y < 0 , then xy *y > 4y. The thing to remember here is that DO NOT multiply an inequality by a variable when you do not know the sign of that variable.

Alternately, what you can do is :

xy < 4 and y >x , ---> as x<y ----> \(x^2 < 4\) (as x<y and xy < 4 ----> \(x^2< xy <y^2\)) ----> -2<x<2 and thus this statement is sufficient to say x<2. Thus B is the correct answer.

Hope this answers your question. _________________

Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink]
18 Jul 2015, 08:52

given: xy<4 ;is x<2?

from(1) y>1=> y can be any +ve number(not specifically Integer);say y= 1.5 than x>2 but if y=3 than x<2 Hence Not sufficient from(2) y>x; Take the worst case when y=x than both will have value 4; but as y grows more than 2 value of x has to go below 2 in order for Y to be greater than x. Since already xy<4 hence x has to be less than 2 Hence Sufficient _________________

Thanks Sindbad ---------------- Click +1 Kudos if my post helped...

gmatclubot

Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x
[#permalink]
18 Jul 2015, 08:52

Interested in applying for an MBA? In the fourth and final part of our live QA series with guest expert Chioma Isiadinso, co-founder of consultancy Expartus and former admissions...